Convergence of a parameter based iterative method for solving nonlinear equations in Banach spaces

2016 ◽  
Vol 67 (1) ◽  
pp. 17-31
Author(s):  
P. Maroju ◽  
R. Behl ◽  
S. S. Motsa
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Nonlinear Equations

scholarly journals A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 83
Author(s):  
José M. Gutiérrez ◽  
Miguel Á. Hernández-Verón
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Integral Equations ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Quadratic Convergence ◽  
Iterative Scheme ◽  
Fredholm Integral Equations

In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations. Therefore, we construct an iterative method with quadratic convergence that does not use either derivatives or inverse operators. Consequently, this new procedure is especially useful for solving non-homogeneous Fredholm integral equations of the first kind. We combine this method with a technique to find the solution of Fredholm integral equations with separable kernels to obtain a procedure that allows us to approach the solution when the kernel is non-separable.

scholarly journals A NOTE ON THE SEMILOCAL CONVERGENCE OF CHEBYSHEV’S METHOD

2012 ◽  
Vol 88 (1) ◽  
pp. 98-105 ◽  
Author(s):  
MANUEL A. DILONÉ ◽  
MARTÍN GARCÍA-OLIVO ◽  
JOSÉ M. GUTIÉRREZ
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Nonlinear Equations ◽  
Semilocal Convergence ◽  
Iterative Processes ◽  
Chebyshev’S Method

AbstractIn this paper we develop a Kantorovich-like theory for Chebyshev’s method, a well-known iterative method for solving nonlinear equations in Banach spaces. We improve the results obtained previously by considering Chebyshev’s method as an element of a family of iterative processes.

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

Sign in / Sign up

Export Citation Format

Share Document